Recent content by Dethrone

1.5 is related to d'Alembert's principle. We can analyze the dynamics of an accelerating frame of reference (i.e non-inertial) by adding a fictitious force. Since the force in system A is $m*100$, then a fictitious force of $m*10$ must be added to system B so that the dynamics in both systems...

A bunch of typos but it's correct. First one it's $3 \cdot (t/3)$, and second one you copied $3e^{-t}$ twice.

I used to have a prof. that would say even 1 + 1 = 2 wasn't obvious to him... to motivate the axiom and properties of real numbers. (Rofl) He would later go on and state trivial limits, etc., basically anything 'obvious', was not obvious to him, to motivate the rigorous treatment of those concepts.

You can't do $\frac{\infty}{\infty}=\infty^{1-1}=\infty^0$ ... that is, treating infinity as if it were a number; otherwise, you'd get all sorts of weird results.

Wait until the velociraptor sleeps, then run out. Maybe I'm thinking about this in the wrong way, but is the motion of the velociraptor deterministic? That is, if I'm at the center of the circle and move along the line connecting the velociraptor and the human, does the velociraptor move left...

Yes Because the oblique asymptote is a line that is neither horizontal (horizontal asymptote) nor vertical (vertical asymptote), but slanted.

It comes right from the identity $\cos\left({\theta+\pi/2}\right)=-\sin\left({\theta}\right)$, or just think about it geometrically. Draw a cosine shifted to the left by $\pi/2$ and compare it with a regular sine wave. Or, apply the cosine addition formulas if you're familiar with them.

It really depends if you assume the question is referring to the same object, otherwise we can argue that one pie could be larger than the other. If we can assume they are different sizes, then what stops us from assuming they have to even be the same object? 2/3 of a pizza vs. 4/6 of a pie. I...

Josh

2. Correct 3. Yes, notice that it's an odd function $f(-x)=-f(x)$ so the "areas" cancel out. 4. Might want to check your math here a bit. The answer is correct ($A=2$), but $B=3$ and $C=-2$. Also, $\lim_{{x}\to{\infty}}(e^{-x})=\lim_{{x}\to{\infty}}1/e^x=0$ since the denominator goes to infinity.

Hi, I guess this could be a rather silly question, but I got a bit confused about the "numerator layout notation" and "denominator layout notation" when working with matrix differentiation...

1. Correct 2. Correct, might want to include units. 3. Correct.

For future reference, there's also Detexify LaTeX handwritten symbol recognition

Are you sure you did not mean $\int \frac{\sqrt{x^2-4}}{x}\,\mathrm{d}x$?

If we let $a$ and $b$ be $n$ dimensional (euclidean) vectors, then your statement follows directly from the reverse triangle inequality, which is a high-school concept. Now if you're asking for the proof of the triangle inequality, since I'm lazy I'll just say it is geometrically intuitive.